Finite Group Databasebeta

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C2×C5×C29×C43⋊C3 #49153447

order37410
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C29×C43⋊C3
unambiguous semidirect product(C2×C43)⋊(C3×C5×C29)
unambiguous semidirect product(C2×C5×C43)⋊(C3×C29)
unambiguous semidirect product(C2×C29×C43)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C29×C43)⋊C3

Splittings

Fitting, socle, HallC2×C5×C29×C43 ⋊ C3
derived, SylowC43 ⋊ C2×C3×C5×C29
HallC5×C29×C43 ⋊ C2×C3
HallC2×C29×C43 ⋊ C3×C5
HallC29×C43 ⋊ C2×C3×C5
HallC2×C5×C43 ⋊ C3×C29
HallC5×C43 ⋊ C2×C3×C29
HallC2×C43 ⋊ C3×C5×C29

Subgroups

subgroupG/H
center, hypercenterC2×C5×C29C43⋊C3
commutator, cosocle, hypocenterC43C2×C3×C5×C29
FrattiniC1G
Fitting, socleC2×C5×C29×C43C3
LCSG ▷ C43
UCSC1 ◁ C2×C5×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12470

Conjugacy classes & character table

4930 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37410, 2);